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Research Papers: Flows in Complex Systems

Numerical Optimization of the Inlet Velocity Profile Ingested by the Conical Draft Tube of a Hydraulic Turbine

[+] Author and Article Information
Sergio Galván

Mechanical Engineering Department,
Universidad Michoacana de
Sán Nicolás de Hidalgo,
Apdo. Postal 588, Col Centro,
Morelia, Michoacán C.P. 58001, Mexico
e-mail: srgalvan@umich.mx

Marcelo Reggio

Mechanical Engineering Department,
École Polytechnique Montréal,
P.O. Box 6000,
Succursale Centre Ville,
Montréal, QC H3C 3A7, Canada
e-mail: marcelo.reggio@polymtl.ca

Francois Guibault

Computer and Software
Engineering Department,
École Polytechnique Montréal,
P.O. Box 6000,
Succursale Centre Ville,
Montréal, QC H3C 3A7, Canada
e-mail: francois.guibault@polymtl.ca

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 25, 2013; final manuscript received February 13, 2015; published online March 19, 2015. Assoc. Editor: Meng Wang.

J. Fluids Eng 137(7), 071102 (Jul 01, 2015) (15 pages) Paper No: FE-13-1339; doi: 10.1115/1.4029837 History: Received May 25, 2013; Revised February 13, 2015; Online March 19, 2015

Past numerical and experimental research has shown that the draft tube inlet velocity is critically important to hydropower plant performance, especially in the case of low-head installations. However, less is known about the influence of flow parameters on turbine performance particularly swirl distribution. Based on the influence of draft tube flow characteristics on the overall performance of a low-head turbine, this research proposes a methodology for optimizing draft tube inlet velocity profiles as a new approach to controlling the flow conditions in order to yield better draft tube and turbine performance. Numerical optimization methods have been used successfully for a variety of design problems. However, addressing the optimization of boundary conditions in hydraulic turbines poses a new challenge. In this paper, three different vortex equations for representing the inlet velocity profile are applied to a cone diffuser, and the behavior of the objective function is analyzed. As well, the influence of the quantitative correlation between the swirling flow at the cone inlet and the analytical blade shape, flow rate, and swirl number using the best inlet velocity profiles is evaluated. We also include a discussion on the development of a flow structure caused by the inlet swirl parameters. Finally, we present an analysis of the influence of flow rate and swirl number on the behavior of the optimization process.

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Figures

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Fig. 1

Inlet velocity profile optimization flow chart

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Fig. 2

The computational domain of the cone

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Fig. 3

Reference velocity profile and its analytical representation

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Fig. 4

Conceptual flow of the MIGA

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Fig. 5

Optimization history of the energy loss factor (ζ) using each of the inlet velocity swirl equations. (a) One vortex, (b) two vortices, and (c) three vortices.

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Fig. 6

Optimization behavior of the energy loss factor (ζ) using the three-vortex equations in terms of the inlet swirling flow. (a) One vortex, (b) two vortices, and (c) three vortices.

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Fig. 7

Optimization behavior of the energy loss factor (ζ) using the three-vortex equations in terms of the normalized flow rate. (a) One vortex, (b) two vortices, and (c) three vortices.

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Fig. 8

Comparison of the optimized inlet velocity profiles obtained from various vortex equations

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Fig. 9

Contours of the axial velocity component on a meridional plane obtained from the various vortex systems. (a) One vortex, (b) two vortices, (c) three vortices, and (d) reference.

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Fig. 10

Contours of the kinetic energy on a meridional plane obtained for the various vortex systems. (a) One vortex, (b) two vortices, (c) three vortices, and (d) reference.

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Fig. 11

Absolute pressure behavior and velocity vectors of the secondary flow as a result of inlet velocity profile on the inlet, middle, and outlet cross sections. (a) One vortex, (b) two vortices, (c) three vortices, and (d) reference.

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Fig. 12

Engineering quantity behaviors along the diffuser length L (m). (a) Axial kinetic energy correction factor, (b) tangential kinetic energy correction factor, (c) swirl number, and (d) momentum correction factor.

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Fig. 13

Flow angle computed from axial and circumferential velocity components in the inlet section for various vortex structures

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Fig. 14

BOPs obtained at different flow rates Qnor for each vortex system

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Fig. 15

Comparison of the inlet velocity profiles obtained without a flow rate constraint (QF) and those obtained with a flow rate constraint: Qnor = 0.5, Qnor = 1.0, and Qnor = 1.5. (a) One-vortex equation (1V), (b) two-vortex equation (2V), and (c) three-vortex equation (3V).

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Fig. 16

Objective function obtained from the BOPs at various flow rates Qnor

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Fig. 17

Comparison of the BOPs and a suitable extrapolation value obtained with various flow rate factors Qnor. (a) One-vortex equation, (b) two-vortex equation, and (c) three-vortex equation.

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